What keeps them from opening all the way? Where do they hit something or bind?

It hits woodwork trim.

You need a Wide Throw hinge. This is a much larger hinge that moves the barrel out to the edge of the trim so the door will swing fully open.

See

http://www.hardwaresource.com/hinges/DOOR+HINGES/Wide+Throw+Hinges+-+Swing+Clear+Hinges/Wide+Throw+Butt+Hinge%2C++Steel

for some info. (And there are many other places to buy) The largest hinge offered at this site will move the barrel out 2 1/8", so you could measure and see if this will work.

The doors should have been installed differently. Should have been moved to the inside so this would not happen.

So that is another option. Have the doors reinstalled.